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1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ... They show up in nature, they show up in math, and they've got some beautiful properties.

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Find the last digit of the 123456789-th Fibonacci number.

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In the Fibonacci sequence, \(F_{0}=1\), \({F_1}=1\), and for all \(N>1\), \(F_N=F_{N-1}+F_{N-2}\).

How many of the first 2014 Fibonacci terms end in 0?

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The Fibonacci sequence is defined by \(F_1 = 1, F_2 = 1\) and \( F_{n+2} = F_{n+1} + F_{n}\) for \( n \geq 1 \).

Find the greatest common divisor of \(f_{484}\) and \(f_{2013}\).

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\[\sum_{n=0}^{\infty} \frac{F_{n}}{3^{n}}= \ ? \]

**Details and Assumptions**

\(F_{n}\) is the \(n^\text{th} \) Fibonacci number, with \(F_{1} = F_{2} = 1\).

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